Fundamentals of Differential Geometry

1. Auflage 1999. Corr. 2. printing 2001
ISBN: 978-0-387-98593-0
Verlag: Springer

Buch, Englisch, 540 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1004 g

Reihe: Graduate Texts in Mathematics

This book provides an introduction to the basic concepts in differential topology, differential geometry, and differential equations, and some of the main basic theorems in all three areas. This new edition includes new chapters, sections, examples, and exercises.

From the reviews: "There are many books on the fundamentals of differential geometry, but this one is quite exceptional; this is not surprising for those who know Serge Lang's books." --EMS NEWSLETTER

Zielgruppe

Graduate

Autoren/Hrsg.

Lang, Serge

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
• Mathematik | Informatik Mathematik Topologie Algebraische Topologie
• Mathematik | Informatik Mathematik Mathematische Analysis

Inhaltsverzeichnis

I General Differential Theory.- I Differential Calculus.- II Manifolds.- III Vector Bundles.- IV Vector Fields and Differential Equations.- V Operations on Vector Fields and Differential Forms.- VI The Theorem of Frobenius.- II Metrics, Covariant Derivatives, and Riemannian Geometry.- VII Metrics.- VIII Covariant Derivatives and Geodesics.- IX Curvature.- X Jacobi Lifts and Tensorial Splitting of the Double Tangent Bundle.- XI Curvature and the Variation Formula.- XII An Example of Seminegative Curvature.- XIII Automorphisms and Symmetries.- XIV Immersions and Submersions.- III Volume Forms and Integration.- XV Volume Forms.- XVI Integration of Differential Forms.- XVII Stokes’ Theorem.- XVIII Applications of Stokes’ Theorem.

Über Autor(innen)